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Lower Confidence Limits (lower + confidence_limit)
Selected AbstractsLower confidence limits for process capability indices Cp and Cpk when data are autocorrelatedQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 6 2009Cynthia R. Lovelace Abstract Many organizations use a single estimate of Cp and/or Cpk for process benchmarking, without considering the sampling variability of the estimators and how that impacts the probability of meeting minimum index requirements. Lower confidence limits have previously been determined for the Cp and Cpk indices under the standard assumption of independent data, which are based on the sampling distributions of the index estimators. In this paper, lower 100(1-,)% confidence limits for Cp and Cpk were developed for autocorrelated processes. Simulation was used to generate the empirical sampling distribution of each estimator for various combinations of sample size (n), autoregressive parameter (,), true index value (Cp or Cpk), and confidence level. In addition, the minimum values of the estimators required in order to meet quality requirements with 100(1-,)% certainty were also determined from these empirical sampling distributions. These tables may be used by practitioners to set minimum capability requirements for index estimators, rather than true values, for the autocorrelated case. The implications of these results for practitioners will be discussed. Copyright © 2008 John Wiley & Sons, Ltd. [source] Estimation of the number of working hours critical for the development of mental and physical fatigue symptoms in Japanese male workers,application of benchmark dose methodAMERICAN JOURNAL OF INDUSTRIAL MEDICINE, Issue 3 2007Yasushi Suwazono PhD Abstract Background To clarify the influence of working hours on subjective fatigue symptoms and obtain the critical dose (number of hours) to determine the number of permissible working hours, we calculated the benchmark dose (BMD) and the 95% lower confidence limit on BMD (BMDL) of working hours for subjective mental and fatigue symptoms using multivariate logistic regression. Methods Self-administered questionnaires were distributed to all 843 male daytime workers aged ,60 years in a single chemical factory, and 715 provided complete replies. The odds ratios of daily working hours were determined using positive findings of the Self-rating Depression Scale and 8 subscales of the Cumulative Fatigue Symptom Index as dependent variables, and other potential covariates as independent variables. Using significant parameters for the working hours and those for other covariates, the BMD and BMDL (BMD/BMDL) values were calculated for corresponding dependent variables. The benchmark response (BMR) was set at 5% or 10%. Results The BMDL with a BMR of 5% was shown to be 9.6,11.6 hr per day, which corresponds to 48,58 working hours per week and 36,78 overtime hours per month. Conclusions These results suggest that special attention should be paid to the workers whose working hours exceed these BMD/BMDL values. Am. J. Ind. Med. 50: 173,182, 2007. © 2007 Wiley-Liss, Inc. [source] A New Method for Constructing Confidence Intervals for the Index CpmQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2004Michael Perakis Abstract In the statistical literature on the study of the capability of processes through the use of indices, Cpm appears to have been one of the most widely used capability indices and its estimation has attracted much interest. In this article, a new method for constructing approximate confidence intervals or lower confidence limits for this index is suggested. The method is based on an approximation of the non-central chi-square distribution, which was proposed by Pearson. Its coverage appears to be more satisfactory compared with that achieved by any of the two most widely used methods that were proposed by Boyles, in situations where one is interested in assessing a lower confidence limit for Cpm. This is supported by the results of an extensive simulation study. Copyright © 2004 John Wiley & Sons, Ltd. [source] Upper susceptibility threshold limits with confidence intervals: a method to identify normal and abnormal population values for laboratory toxicological parameters, based on acetylcholinesterase activities in sea licePEST MANAGEMENT SCIENCE (FORMERLY: PESTICIDE SCIENCE), Issue 3 2006Anders Fallang Abstract The interpretation and importance of comparing field values of susceptibility to pesticides with a laboratory reference strain that might bear little resemblance to the actual situation in the field are problematic and a continuing subject of debate. In this paper a procedure for defining a ,normal sensitive' population from a field study of 383 individuals to provide a basis for analysing and interpreting in vitro results is described and examined. Instead of using only the 95th percentile, the upper and lower confidence limits for the 95th percentile were also compared to select the best estimation of the limit for the normal material. A field population constrained by the upper confidence limit for the 95th percentile provides appropriate descriptions of the normal material in this study. This approach should prove useful in studies of pesticide resistance in field populations. Copyright © 2006 Society of Chemical Industry [source] A New Method for Constructing Confidence Intervals for the Index CpmQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2004Michael Perakis Abstract In the statistical literature on the study of the capability of processes through the use of indices, Cpm appears to have been one of the most widely used capability indices and its estimation has attracted much interest. In this article, a new method for constructing approximate confidence intervals or lower confidence limits for this index is suggested. The method is based on an approximation of the non-central chi-square distribution, which was proposed by Pearson. Its coverage appears to be more satisfactory compared with that achieved by any of the two most widely used methods that were proposed by Boyles, in situations where one is interested in assessing a lower confidence limit for Cpm. This is supported by the results of an extensive simulation study. Copyright © 2004 John Wiley & Sons, Ltd. [source] LOWER BOUNDS TO THE POPULATION SIZE WHEN CAPTURE PROBABILITIES VARY OVER INDIVIDUALSAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2008Chang Xuan Mao Summary The problem of estimating population sizes has a wide range of applications. Although the size is non-identifiable when a population is heterogeneous, it is often useful to estimate the lower bounds and to construct lower confidence limits. A sequence of lower bounds, including the well-known Chao lower bound, is proposed. The bounds have closed-form expressions and are estimated by the method of moments or by maximum likelihood. Real examples from epidemiology, wildlife management and ecology are investigated. Simulation studies are used to assess the proposed estimators. [source] Multiplicity-Adjusted Inferences in Risk Assessment: Benchmark Analysis with Quantal Response DataBIOMETRICS, Issue 1 2005Daniela K. Nitcheva Summary A primary objective in quantitative risk or safety assessment is characterization of the severity and likelihood of an adverse effect caused by a chemical toxin or pharmaceutical agent. In many cases data are not available at low doses or low exposures to the agent, and inferences at those doses must be based on the high-dose data. A modern method for making low-dose inferences is known as benchmark analysis, where attention centers on the dose at which a fixed benchmark level of risk is achieved. Both upper confidence limits on the risk and lower confidence limits on the "benchmark dose" are of interest. In practice, a number of possible benchmark risks may be under study; if so, corrections must be applied to adjust the limits for multiplicity. In this short note, we discuss approaches for doing so with quantal response data. [source] | ||||||||||